Geometry Skills

Throughout this whole semester I feel I have learned many things. Such as Fractals, Polygons, Pythagorean theorem, logic, and how to work out word problems. Out of all these subjects, Pythagorean Theorem I have mastered the most and has stuck with me the most so far this year. A lot of the POW's(Problem of the week) that we did during that time had to do with Pythagorean Theorem and some still do involve Pythagorean Theorem. I think having that much practice has given me the chance of getting comfortable with it and has got me to the point of mastery. I know I have mastered Pythagorean Theorem because when I get any problem in school that has anything to do with a triangle I know exactly what to do and when to do it. I know how to find any missing sides and to see if the triangle is an actual right triangle, since Pythagorean theorem only applies to right triangles.

In math class we have this work sheet that we get twice a week, called an exploration. Explorations is 6 to 7 math problems that you must solve before the next day. Explorations usually go over what we are learning in class. the next when we come to class we go over them in a table group, which is really helpful. It allows you the time to see what other people did and how you might have gone wrong or where someone else went wrong. This way we can fix what we did or help someone else fix what they did before we turn it in. I believe if we don't go over it in class with others, I wouldn't learn as much and I wouldn't benefit as much if I just turned it in with out discussing our answers. Going over them in class can also end in a challenge because sometimes we can't reach an agreement on what the answer actually is or everyone is stuck on the same problem.

One of the biggest break through moments I've had this year was when we were working on Logic. At first I didn't really understand how to solve logic and if logic was truth or false. Once Aliza started to teach what each statement is and which statements are logical equivalent everything started to come together. Then when the actual break through happened was when I learned the statements in P-Q form, I think seeing it in a different way, showed me a different perspective and really helped me.

Evidence

For the POW below I had to use Pythagorean theorem to find the hypotenuse of PQU and TSR and then I created another triangle to find what the the length of QR was. QR was the hypotenuse of the new triangle so again I used Pythagorean theorem.

For POW number 2 to find perimeter of ABCD I had to find the hypotenuse of ABC first by using Pythagorean theorem. once I found the hypotenuse of that triangle it helped me find the Hypotenuse of ACD because it gave me another side length to work with. So I used those two side lengths and put them in Pythagorean theorem, which found the length of AD. Know that I knew all the sides I could finish the POW and find the perimeter of the whole shape, ABCD.

I feel this POW shows that I've mastered Pythagorean theorem because even though we aren't working on Pythagorean theorem I know how to use it problems, like this POW. In this POW i may not have gotten everything right, but I did use Pythagorean theorem to find the hypotenuse of ADF and GCB. Getting those two lengths helped find the area of the triangle AEB. I feel this POW is incorrect not because of the Pythagorean theorem, but because once I found those things I didn't know what to do next.

I feel this Exploration really helped me when we were learning Logic. this work sheet has all things that we went learned in class. It allows us to write the logic and see if its true, instead of just looking at a logic statement someone already wrote. It allowed me to work with the P-Q statements and just with normal statements. I think having the different logic statements, such as the converse, inverse, contrapositive, negation, and conditional also helped me have a breakthrough moment.

Problem-Solving Skills

In Geometry we have these things called Habits of a Mathematician. In the Habits of a Mathematician there is generating ideas, communicating thinking in a clear and accessible way, recognizing and resolving errors, and reflecting and synthesizing. In my opinion so far this year I have mastered generating ideas out of all the Habits of a Mathematician. I feel this is the one I've mastered because when ever I get a math problem I also look at different ways to solve that problem. I try different methods to get that answer and sometimes it takes more then one idea or method to get the answer. the POW's and explorations have really helped me get this skill down. The POW's cause you to think of many different ways to solve it and the eventually you get to the final way that works.

One Habit of a Mathematician that I could probably improve on and try to use more often in math is communicating thinking in a clear and accessible way. The only time I use this habit is when I do POW's. Part of the POW is to restate the question in a different way that helps you understand the problem. I never try to restate the question when I don't get what it's asking, I ask someone else what it means and what we are supposed to do.

Evidence

For this POW in order to find the solution i had to try different methods to get the answer perfect. It took me over ten different methods before I final got it. I first tried putting the cards every other, so it was A,6,2,7,3,8,4,9,5,10. this worked up until I got five. I tried mixing up all the numbers, that didn't work. So I kept just trying to switch around the number 6,7,8,9,10 and eventually I got it.

In each POW that we do apart of the outline is to re-word the question. In the example I re-worded it by putting into two parts because that's how it made it easier for me to understand. That I should first try to solve the first part and then move on to solving the second part of the question. I feel I only do this in POW's because it is required of me to. I don't find the need of re-wording a question, I try to find a way to work around it.

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